Corticotrophs We have extended our modeling work on pituitary cells to include a model of corticotrophs, which secrete ACTH and play an important role in the response to stress. A previous model by others had centered on the effect of CRH to convert spontaneous spike activity to bursting activity, which may promote increased cytosolic calcium and thereby the increased ACTH secretion induced by CRH. The proposed mechanism for the initiation of bursting was the activation of a large conductance voltage- and calcium-activated potassium channel (BK). We had a more diverse data set, indicating that unstimulated cells may be quiescent as well as spiking, and that CRH sometimes induced spiking rather than bursting. In addition, BK channels are not well suited to depolarizing silent cells, so we developed a more comprehensive model to account for the greater diversity of activity patterns (Reference #1). This model also showed, among other things, that other channels than BK, such as a background, voltage-independent sodium channel, could mediate a transition from silent or spiking behavior to bursting. This suggests that CRH may have more than one channel target. The enhanced corticotroph model revealed further that the results of modifying the activity of ion channels is context dependent, i.e. it depends on the other ion channels in the cell and their expression levels. The data and the model together also demonstrated that corticotrophs are special among pituitary cells in having more diverse patterns of activity. Whereas other pituitary cells generally either spike or burst when active, pituitary cells can do either, depending on the quantitative balance of channels present. This led us to hypothesize that corticotrophs or corticotroph-like precursors arise early in pituitary development and then give rise to the other cell types by losing particular functions. Losing BK channels gives rise to an electrical pattern resembling that of gonadotrophs (spiking), and losing voltage-dependent sodium channels gives rise to a pattern resembling that of lactotrophs and somatotrophs (bursting). We laid out this hypothesis in a review article for a special issue of Molecular and Cellular Endocrinology (Reference #2). Of course, pituitary cells differ not only in electrical pattern but also in hormones secreted and expression of receptors for hormones and peptides that regulate secretion. Further work is called for to establish how receptor, hormone and ion channel expression are varied in a coordinated way in development to produce the integrated phenotypes. The detailed results of studying pituitary development may shed light on other tissues composed of related but distinct cell types, such as pancreatic islets. Purinergic Receptors: Purinergic (P2X) receptors are ligand-gated ion channels that carry calcium into cells when they bind, for example, ATP. They play numerous roles in neurons and other cell types, such as mediating cell survival/cell death decisions and pain pathways. A polymorphism in the P2X7 receptor has been proposed as a susceptibility gene for the NOD mouse, a model for type 1 diabetes.Over the last decade we have used experiments and modeling to show that several P2X subtypes, P2X2, P2X4 and P2X7, can be modeled by a common core of channel states in spite of divergent behavior. For example, P2X7 dramatically increases its current upon prolonged or repeated exposure to ATP (potentiation), whereas P2X4 decreases its current over time (desensitization). The model showed that P2X4 likely shares with P2X7 the ability to increase its conductance but that it is masked by desensitization. P2X4 usually resembles P2X2 in desensitizing, but it can be potentiated when it binds to ivermectin, an anti-parasitic drug. We modeled this behavior using the common core model (2015 report) but found that to get subtle details of the response correct, a more detailed model was required. We used an advanced technique, Markov Chain Monte Carlo, to fit this more complex model to the data and resolve several controversies about the regulation of this channel type. Neuronal Adaptation: Many neurons maintain low frequency firing rates in the face of strong stimuli by means of negative feedback provided by adaptation currents, such as calcium-activated potassium current. A major paradigm shift 20 years ago was initiated by Rinzel and Ermentrout, who showed that a particular kind of firing threshold mediated by a bifurcation called a SNIC (saddle node on an invariant circle) could produce low-frequency firing with any adaptive current. However, such low rates only hold in a narrow range of stimulus. Mathematically, the frequency-current response curve (f-I curve) is very steep at the threshold. In order to broaden the range to produce robust low frequency firing, an adaptation current is still needed. Ermentrout (Neural Comput. 10(7):1721-1729, 1998) showed that adaptation generically linearizes the f-I curve when a SNIC is present in the raw system (without adaptation). We revisited this and found that whereas a SNIC contributes to linearization, in practice linearization over a large interval may require strong adaptation strength. Moreover, we found that sufficiently strong adaptation can linearize the f-I curve even when a SNIC is absent. The work is described in Ref. #4.